二项式定理+前缀Sigma

Posted 2022-10-29 --hpy-7m

https://hihocoder.com/problemset/problem/1430

思路：

要用前缀去推Sigma总公式，比较方便。https://blog.csdn.net/weixin_37517391/article/details/83821752

  1 #define ios ios_base::sync_with_stdio(0); cin.tie(0);
  2 #include <cstdio>//sprintf islower isupper
  3 #include <cstdlib>//malloc  exit strcat itoa system("cls")
  4 #include <iostream>//pair
  5 #include <fstream>//freopen("C:\\Users\\13606\\Desktop\\草稿.txt","r",stdin);
  6 #include <bitset>
  7 //#include <map>
  8 //#include<unordered_map>
  9 #include <vector>
 10 #include <stack>
 11 #include <set>
 12 #include <string.h>//strstr substr
 13 #include <string>
 14 #include <time.h>//and(((unsigned)time(NULL))); Seed n=rand()%10 - 0~9;
 15 #include <cmath>
 16 #include <deque>
 17 #include <queue>//priority_queue<int, vector<int>, greater<int> > q;//less
 18 #include <vector>//emplace_back
 19 //#include <math.h>
 20 //#include <windows.h>//reverse(a,a+len);// ~ ! ~ ! floor
 21 #include <algorithm>//sort + unique : sz=unique(b+1,b+n+1)-(b+1);+nth_element(first, nth, last, compare)
 22 using namespace std;//next_permutation(a+1,a+1+n);//prev_permutation
 23 #define rint register int
 24 #define fo(a,b,c) for(rint a=b;a<=c;++a)
 25 #define fr(a,b,c) for(rint a=b;a>=c;--a)
 26 #define mem(a,b) memset(a,b,sizeof(a))
 27 #define pr printf
 28 #define sc scanf
 29 #define ls rt<<1
 30 #define rs rt<<1|1
 31 typedef long long ll;
 32 void swapp(int &a,int &b);
 33 double fabss(double a);
 34 int maxx(int a,int b);
 35 int minn(int a,int b);
 36 int Del_bit_1(int n);
 37 int lowbit(int n);
 38 int abss(int a);
 39 const double E=2.718281828;
 40 const double PI=acos(-1.0);
 41 //const ll INF=(1LL<<60);
 42 const int inf=(1<<30);
 43 const double ESP=1e-9;
 44 const int mod=(int)1e9+7;
 45 const int N=(int)5e4+10;
 46 
 47 long long C[110][110];
 48 void Init() 
 49     C[0][0] = 1;
 50     for(int i = 1;i <= 100;++i) 
 51         C[i][0] = 1;
 52         for(int j = 1;j <= i;++j) 
 53             C[i][j] = (C[i-1][j-1] + C[i-1][j]) % mod;
 54         
 55     
 56 
 57 //======================================================Cnk预处理;
 58 ll S[105][N],SS[105][N],ans[N];
 59 char s[N];
 60 
 61 void solve()
 62 
 63     ll n,k;
 64     sc("%lld%lld",&n,&k);
 65     sc("%s",s);
 66 
 67     for(int i = 0;i <= n;++i) S[0][i] = 1;
 68     for(int i = 1;i <= n;++i) S[1][i] = (s[i-1]-‘0‘) + S[1][i-1] ;
 69     for(int i = 2;i <= k;++i)
 70         for(int j = 1;j <= n;++j)
 71             S[i][j] = S[1][j] * S[i-1][j] % mod;
 72 
 73     SS[0][0] = 1;
 74 
 75     for(int i = 0;i <= k;++i) 
 76         for(int j = 1;j <= n;++j)
 77             SS[i][j] = (SS[i][j-1] + S[i][j])%mod;
 78     
 79 
 80     for(int i=1;i<=n;++i)
 81     
 82         ll sum=0;
 83         for(int j=0;j<=k;++j)
 84         
 85             ll temp=C[k][j]*S[k-j][i]%mod*SS[j][i-1]%mod;
 86             if(j&1)
 87                 sum=(sum-temp+mod)%mod;
 88             else
 89                 sum=(sum+temp)%mod;
 90         
 91         ans[i]=sum;
 92     
 93     for(int i=1;i<=n;++i)
 94         pr("%lld%c",ans[i],i==n?‘\n‘:‘ ‘);
 95 
 96 
 97 int main()
 98 
 99     Init();
100     int T;
101     sc("%d",&T);
102     while(T--)solve();
103     return 0;
104 
105 
106 /**************************************************************************************/
107 
108 int maxx(int a,int b)
109 
110     return a>b?a:b;
111 
112 
113 void swapp(int &a,int &b)
114 
115     a^=b^=a^=b;
116 
117 
118 int lowbit(int n)
119 
120     return n&(-n);
121 
122 
123 int Del_bit_1(int n)
124 
125     return n&(n-1);
126 
127 
128 int abss(int a)
129 
130     return a>0?a:-a;
131 
132 
133 double fabss(double a)
134 
135     return a>0?a:-a;
136 
137 
138 int minn(int a,int b)
139 
140     return a<b?a:b;
141